Undecidability of intuitionistic theories formulated with the apartness relation
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چکیده
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Sequent calculus proof theory of intuitionistic apartness and order relations
Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved. Among the consequences of the result is the disjunction property for these theories. Through methods of proof analysis and permutation of rules, we establish conservativity of the theory of apartness over the theory of equality defined as the negation of apar...
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The theories of apartness, equality, and n-stable equality are presented through contractionand cut-free sequent calculi. By methods of proof analysis, a purely proof-theoretic characterization of the equality fragment of apartness is obtained. Philosophia Scientiæ, Cahier spécial 6, 2006, 61–79. 62 Bianca Boretti and Sara Negri
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Many classes of structures have natural functions and relations on them: concatentation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study the (un)decidability of the theory of several natural classes of structures with appropriate functions and relations. For some of these classes of structures, the resulting theory is decidable; for...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1977
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-97-1-17-36